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Abstract

The
classic regelation experiment of Thomson in the 1850s deals
with cutting an ice cube, followed by refreezing. The cutting was
attributed to pressure-induced melting but has been challenged continuously,
and only lately consensus emerged by understanding that compression
shortens the O:H nonbond and lengthens the H–O bond simultaneously.
This H–O elongation leads to energy loss and lowers the melting
point. The hot debate survived well over 150 years, mainly due to
a poorly defined heat exchange with the environment in the experiment.
In our current experiment, we achieved thermal isolation from the
environment and studied the fully reversible ice–liquid water
transition for water confined between graphene and muscovite mica.
We observe a transition from two-dimensional (2D) ice into a quasi-liquid
phase by applying a pressure exerted by an atomic force microscopy
tip. At room temperature, the critical pressure amounts to about 6
GPa. The transition is completely reversible: refreezing occurs when
the applied pressure is lifted. The critical pressure to melt
the 2D ice decreases with temperature, and we measured the phase
coexistence line between 293 and 333 K. From a Clausius–Clapeyron
analysis, we determine the latent heat of fusion of two-dimensional
ice at 0.15 eV/molecule, being twice as large as that of bulk
ice.

Water at
atmospheric conditions
exists in several states of aggregation, such as vapor, liquid, and
several amorphous and crystalline solid phases.1−4 Understanding the vast amount
of ice phases and phase transitions is essential for many fields,
including environmental, life, and planetary sciences.5,6 The most important phase transitions are those of melting and freezing
of water because they define the sea level and dominate life on Earth.7 One of the anomalous thermodynamic properties
of water is that its melting point decreases as the pressure increases.8−11 This effect is of particular importance because it can define water
flow under large compressive forces. Pressure-induced melting plays
a prominent role in glacial motion.12−14 The weight of massive
glaciers can cause internal deformations on the ice structure. The
effect is strongest near the glacier/terrain interface, where pressures
are highest. At these locations, ice melts even at temperatures below
its bulk melting point, and the resulted liquid form of water allows
the glacier to slide over the terrain.

It was initially believed
that moderate pressures were sufficient
to form a thin water layer on ice, attempting this way to explain
the anomalous friction behavior of ice, for example, during ice skating.15 However, this idea was already challenged early
on by Faraday.16 Slipperiness of ice (for
example, in ice skating applications) is the result of the presence
of a liquid-like film of water on the ice surface, even at temperatures
below its freezing point.17−19 Pressure-induced melting of ice
requires far greater pressures than those encountered in common slippery
situations. Another example that is often associated with ice skating
is Thomson’s 19th century experiment that involves the sintering
of a wire through an ice cube (or a large block of ice),16,20 the wire cuts through the ice by melting it by the application of
an external force. As the wire moves through, the water behind it
immediately refreezes. Ice melting due to the application of a high
external pressure and refreezing when the pressure is relieved is
known as regelation. Thomson’s experiment is often used as
a textbook paradigm for pressure-induced melting and regelation.21,22 However, even though pressure-induced melting is real when sufficiently
high pressures are applied (in the order of hundreds of MPa or a few
GPa), the wire that cuts through a block of ice is a far more complicated
experiment and several other parameters contribute to the melting
process. Among those, heat conduction through the wire, friction heating,
and wire wettability contribute the most.11,23,24 Even though it is difficult to experimentally
decouple pressure-induced melting from other effects, it still plays
a prominent role in several physical processes. It is most prominent
in systems in which large pressures prevail. Such systems are difficult
to access experimentally, and knowledge on the molecular dynamics
comes only from theoretical investigations.11,25,26 It is thus highly desirable to find a way
to access pressure-induced melting experimentally.

We have designed
an experiment that allows for the first time to
explore the microscopic behavior of ice layers under an external pressure.
Our solution suppresses possible disturbing thermal influences from
the environment. We use graphene as an ultrathin coating to trap water
structures on a supporting mica surface. Because of graphene’s
unusual properties, such as impermeability to small molecules, mechanical
flexibility, and chemical stability, it allows for the direct visualization
of confined water structures by scanning probe techniques.27 The anisotropy in the thermal conductivity of
graphene28 and mica,29 with a high/low conductivity parallel/perpendicular to
the sheets, allows one to investigate the intrinsic properties of
the ice network, isolated from thermal fluctuations during imaging.
A sharp atomic force microscopy (AFM) tip is used to raster-scan the
graphene surface on top of ice crystals on mica. By regulating the
tip load, we can directly control the locally applied pressure at
the graphene/ice/mica interface with nanometer precision and high
accuracy. Any heat induced by the scanning AFM tip is quite rigorously
led away from the ice crystals due to the extremely low thermal conductivity
perpendicular to the graphene sheets as the in-plane thermal conductivity
outweighs by far the out-of-plane thermal conductivity (2000–4000
and 6 Wm–1 K–1, respectively).28 The system is therefore a viable candidate to
investigate pressure-related phase transitions of ice networks decoupled
from thermal effects.

Graphene coating of water has provided
useful insight on intercalation
effects and on the physical properties of confined water structures.27,30−41 In principle, when water is confined between two flat surfaces,
its structure and dynamics depend heavily on the molecular structure
of the confinement walls, the confinement dimensions, temperature,
and pressure.42−48 Often, confined water structures display perpendicular order due
to stratification effects at the vicinity of the surface.49−51 In particular, water confined between graphene and mica forms flat
islands with faceted edges and well-defined thickness, close to the
interlayer distance of Ih ice.27 These water structures are in equilibrium with the environmental
water pressure, and they communicate with the environment through
defects located at the graphene/mica interface.33 At ambient relative humidity (~50%), the graphene/mica
confinement contains a thin water film with a thickness that corresponds
to two water layers.52,53 Interestingly, at low relative
humidity (<1%), ice crystals grow at the interface induced by the
heat extracted from the system by the evaporation of water molecules
from the intercalated water film.53 Because
of diffusion and rotational limitations of the water molecules that
want to incorporate into the ice crystal, the crystallites acquire
a fractal shape (see Figure ​Figure11a).54 The mica is hydrophilic and
defines the structure of the ice crystal, whereas the graphene is
slightly hydrophobic and acts as a neutral confinement. First-principle
molecular dynamics (MD) simulations revealed that the first water
monolayer is a fully connected hydrogen bonded network epitaxially
grown on mica.55,56 The first ice layer on mica (and
in contrast to multilayer films) has no free O−H bonds sticking
out of its surface.55,57,58 The ice layer possesses a net dipole moment where the positive side
points toward the mica surface. A schematic of this confined ice network
is shown in Figure ​Figure11b, and the structure is based on ref (55). Owing to the absence of uncoordinated O−H
bonds on the surface of the ice layer and the appearance of a net
dipole moment, a graphene covering these ice films is p-type doped.53,59

Structure
of water intercalated between graphene and mica. (a)
AFM topographic image (1.5 × 1.5 μm2) of ice
crystals (bright region) confined between graphene and the supporting
mica, surrounded by two water layers (dark region). (b,c)...

Here, we report on ice melting induced by the application
of an
external pressure. We show that the ice crystals melt when subjective
to high external pressures and refreeze when the pressure is lifted,
coined as regelation. For local pressures higher than 6 GPa, a solid
to quasi-liquid transition takes place. The water molecules of the
ice crystal become dynamic, and the layer loses its net dipole moment,
indicative of disorder. The ice crystals start to melt initially at
their edges, and the quasi-liquid layer expands toward their interior.
The process is fully reversible when the applied pressure is released,
and the water molecules immediately refreeze and reform a polarized
ice layer. Our experiments are of interest to water (flow) in biological
and geological systems. They also expand on the complex phase diagram
of confined ice between graphene and mica.

Results and Discussion

Pressure-Induced
Solid to Quasi-liquid Phase Transition

When the graphene/water/mica
system is exposed to low relative humidity,
ice crystals are formed at the graphene/mica interface induced by
the heat extracted from the system due to water evaporation into the
environment.53 An example is shown in the
AFM topographic image shown in Figure ​Figure11a, where the ice crystals (shown as bright areas) have
a fractal shape. The surrounding brighter area is a double layer water
film (see Figure ​Figure11c);
the height difference between the two levels in this image amounts
to 0.36 ± 0.02 nm, a value very close to the interlayer distance
of Ih ice (hexagonal ice). The structure of the ice crystal
is shown schematically in Figure ​Figure11b. Besides the ice crystals and the water bilayer,
small droplets of water are occasionally present on top of the water
double layer, as shown, for instance, in Figure ​Figure22a. The simultaneously recorded lateral force
microscopy (LFM) image displays a difference in roughness between
graphene on top of the ice layer and the surrounding water double
layer. The higher roughness of graphene on top of the ice fractal
was attributed to the presence of potassium ions and ionic domains
on the air-cleaved mica surface (we note that the topography is featureless).59 The same structure is also present in the double
water layer, however, less pronounced as a result of convolution by
the second water layer. These images were obtained in contact mode
AFM with a tip load of approximately 0.8 nN. By considering a p-doped
diamond tip with a radius of curvature of about 5 nm, the applied
pressure on the graphene/ice/mica system induced by the tip is approximately
4.5 GPa, calculated using the Hertz model.60−62

Therefore, by scanning the surface
in contact mode and varying
the tip load in a controlled way, we can obtain spatial information
about the aggregation state of the confined water structures as a
function of the applied pressure. We find that when the pressure exceeds
a critical value (Pc), the ice/water edges
become fuzzy and dynamic. These edges change from frame to frame even
when the pressure is kept constant and higher than Pc. In addition, a quite faint but strongly persistent
contrast appears that propagates from the edges of the ice crystal,
visible in both topographic and LFM images (Figure ​Figure22b,c and their insets). The contrast is stronger
in the LFM images. Under these conditions, the edges of this region
are dynamic (see Figure ​Figure22h and compare it to Figure ​Figure22g, i.e., a zoom-in of Figure ​Figure22a) and change shape every consecutive image,
even when the pressure remains at a constant value. Furthermore, the
area it occupies strongly depends on the applied pressure. As the
pressure increases, this region propagates further toward the interior
of the (dark) ice layer; this becomes clear upon comparing, for example,
panels c and d of Figure ​Figure22, and the total area that it occupies increases further (see
the movie in the Supporting Information for more details). The dynamic nature of this region suggests that
the water molecules at this location are mobile. Based on this dynamic
behavior, we will hereby refer to this region as a quasi-liquid water
layer. Additional proof will be presented further below.

When
the pressure is reduced, the area of the quasi-liquid layer
shrinks, starting first from the interior of the ice crystal (Figure ​Figure22d,e). The process
is fully reversible, meaning that the molten area disappears completely
when the pressure drops below a certain threshold (<6 GPa). In
addition to the disappearance of the quasi-liquid layer, the ice/double
layer of water edges become stable and smooth when the pressure is
decreased; see the red arrows in Figure ​Figure22f. Moreover, the density of small water droplets
found on top of the surrounding water layers has increased, suggesting
mass transport (see Figure ​Figure22f and compare it to 2a). Note that after the pressure is lifted,
the total ice area has increased, accompanied by a decrease of the
double water layer area. The excess amount of water molecules form
a third water “layer” or droplets on top of the double
layer (mass conservation). Regions that were not scanned with a high
tip load remained unaltered (see Figure ​Figure22a,f, outside the white dashed square). We
emphasize that the melting of the ice crystals is heterogeneous, as
it only occurs locally at the region of high pressure just below the
surface of the AFM tip. As the tip moves across the graphene surface,
the water is expected to refreeze at the locations left by the tip.
At the locations where the pressure is lifted, refreezing should occur
with a finite speed, that is, slower than the AFM scanning speed (the
refreezing rate is low compared to the scan speed for a single line,
0.5 s, but faster than the acquisition time of one image, 256 s).

Figure ​Figure33a shows
topographic information on an area consisting of the quasi-liquid
layer, ice layer, and the double water layer. Marked with the white
dashed line in Figure ​Figure33a, the line profile provides a quantitative measurement of the depth
of the fractal with respect to the double layer of water, i.e., 0.36 ± 0.02 nm, which is in good agreement with
previous studies.34,52,53 A histogram of the line profile is shown in Figure ​Figure33c and reveals a third peak which corresponds
to the evolved quasi-liquid layer. This layer is approximately 70
± 5 pm higher than the ice crystal. The increase of height is
a result of the disordered water network, which is in direct contrast
to the H-down network of the ice crystal (Figure ​Figure11b). The disorder results in several OH bonds
that point away from the mica surface and increase the average thickness
of the quasi-liquid layer.

Supporting evidence that the evolved dynamic region is a
quasi-liquid
layer of water is obtained from LFM measurements (see insets in Figure ​Figure22b–g). Strikingly,
the lateral deflection of the cantilever as measured by the LFM signal
(which is proportional to tip–surface friction) increases at
the regions where graphene covers the dynamic water layer by about
10%. This is rationalized by the fact that in these regions it is
easier to deform the graphene cover in a vertical sense (owing to
the mobile nature of the water molecules at these locations). These
indentations give then rise to enhanced resistance when the tip is
moved parallel to the surface. On the other hand, graphene in contact
with ice can be less easily indented, which gives rise to lower friction
forces, in line with the observations.63,64 We emphasize
that the LFM images very clearly show the existence of melted ice
and the extension of its area. These regions are also visible in topography
images, but the contrast is rather weak and the exact area of the
melt is sometimes harder to detect due to strong contrast enhancement
actions.

Emerging Disorder in the Quasi-liquid Layer

In a previous
study, we showed that the graphene cover can be doped by the underlying
ice/water structures.59 That investigation
made it possible to gain information about the structure of the ice
crystal and the double water layer. The graphene on top of an ice
crystal is p-doped, where on the other hand the double water layer
does not induce any significant charge doping on the graphene cover
because of disorder. The p-doping is the consequence of the crystalline
structure of the ice, which has a H-down configuration with a net
dipole moment,55,56,58 whereas the net dipole moment is absent in the water double layer.
In essence, the ice surface is electronegative, and the graphene is
doped due to charge transfer.65 This difference
in charge can be measured using a conductive AFM.59Figure ​Figure44a and its inset show a topography and a conductive AFM image of an
ice crystal intercalated between graphene and mica, under 4.5 GPa
of applied pressure (the pressure is small enough that it does not
induce any changes in the ice crystal) at room temperature. No bias
was applied between the conductive AFM tip and the substrate. Instead,
only charges that are present on or near the surface can be detected
by the AFM tip and measured in the current signal. A distinct correlation
is found between the topography and the current image. The graphene
layer on top of the ice layer displays a significant amount of current
(yellow), whereas graphene above the double layer shows almost no
current (blue). In order to enhance the correlation, the topography
and the current images are overlaid in Figure ​Figure44b. Clearly, all the yellow parts (high current)
are located within the borders of the ice fractal.

Graphene conductance
and its relation to the water structure. (a)
Topography image (190 × 190 nm2) of an ice crystal
intercalated between graphene and mica at room temperature when the
tip load is 0.8 nN (which corresponds to 4.5 GPa). As can...

When pressures larger than 6 GPa are applied on the ice crystals,
a phase transition takes place and a quasi-liquid layer is formed
(see Figure ​Figure44c: slightly
brighter areas within the ice fractal). Exactly at the places where
the quasi-liquid layer is formed, the current measured with the conductive
AFM (C-AFM) vanishes. When the two images are overlaid, the change
in charge density becomes even more prominent (as shown in Figure ​Figure44d). This can only
be explained by a change in the structure of the underlying ice crystal.
As mentioned earlier, the water network in the ice has a H-down configuration,
which results in a net dipole moment (Figure ​Figure44f).55 The quasi-liquid
layer, as a result of disorder, loses its net dipole moment, and therefore
no current/charge is measured on the graphene cover (Figure ​Figure44g).56 In Figure ​Figure44e, the
cross-correlation between the topography and the current image is
shown. A distinct decrease of the correlation is observed as a function
of the applied pressure. This declining in overlap is the expected
result because, with increasing pressure, an increasing fraction of
the ice layer is melted. As explained above, the melted regions do
not contribute to the conduction.

To summarize the above observations,
when the pressure exerted
on the confined ice exceeds a specific threshold, the ice/water edges
become very dynamic and a dynamic layer appears at the interface.
This layer is thicker than the ice layer by 70 ± 5 pm. This region
increases in lateral size with increasing pressure. Owing to the dynamic
nature of this layer, the observed disorder, and the high apparent
mobility of the water molecules, we refer to it as a quasi-liquid
water layer. We expect that this layer preserves some slight order
that is stemming from the underlying mica due to stratification effects
(see Figure ​Figure44g). We
have thus shown that pressure variations can induce morphological
changes in confined ice nanocrystals. The ice crystals melt when a
high pressure is exerted at the interface by an AFM tip. When the
pressure is lifted, the newly formed quasi-liquid layer refreezes.
Our experiments provide the first ever example of regelation, fully
decoupled from thermal effects owing to graphene’s large anisotropy
in the thermal conductivity, which warrants very good isolation form
the environment. Heat that might be induced by frictional forces is
immediately transported away from the underlying water structures,
owing to the high in-plane thermal conductivity. This leaves pressure
as the sole parameter responsible for the observed phase transitions.

The observed quasi-liquid layer shows similarities with the structure
found by Li et al. on water on mica.56 The authors performed ab initio molecular
dynamics study of the structural and dynamic properties of water adlayers
on the mica surface56 at different temperatures.
They found that at room temperature molecules that are bonded to the
mica form an ice network, where the water molecules bridging the K+ ions are slightly weaker bonded than those bonded directly
on the mica oxygen ions. When the system is brought to elevated temperatures,
the structure starts to show melting behavior. Even though the hydrogen
network collapses at these temperatures, the hydrogen bonds between
the water and the supporting mica can remain. The bridging water molecules
can easily rotate and diffuse, resulting in a liquid-like layer. Of
course, in our system, the temperature remains constant and cannot
be made accountable for the observed phase transition. We thus propose
that the H2O molecules behave similarly when an external
pressure is applied. When water is compressed, the O:H hydrogen bond
shortens and stiffens; on the other hand, the O–H covalent
bond elongates and softens via O–O repulsion.26 The elongation of the covalent bond and its
energy loss lowers the melting point. Once the pressure is reduced,
the H:O–H bond fully recovers to its original state.25

Graphene Thickness Dependence

It
is evident from the
AFM images in Figure ​Figure22 that the quasi-liquid layer emerges at approximately 6 GPa, and
its area increases in size when the external pressure is increased.
The area of the quasi-liquid layer (AQL) is measured for each frame and plotted as a function of the applied
pressure in Figure ​Figure55a. The quasi-liquid layer area increases with increasing pressure
until a maximum of 0.25 μm2 (~95% of the total
ice area) at a pressure of approximately 10 GPa. We note here that
melting does not occur instantaneously everywhere in the image; these
variations might originate from the non-homogeneous distribution of
the potassium ions on the mica surface59 that could influence the bonding of the water network.56 When the pressure is decreased, the quasi-liquid
area decreases until it completely vanishes. The molecules immediately
refreeze and resume their positions in a polarized ice layer (see Figure ​Figure44a).

Influence of the graphene
layer thickness on the melting behavior
of confined ice. (a) Quasi-liquid layer area as a function of the
applied pressure. The area of the quasi-liquid layer increases with
increasing applied pressure and completely vanishes...

The same behavior is observed when the ice crystals
are covered
with thicker graphene covers. However, the applied force needed to
create the quasi-liquid layer increases with the graphene thickness.
For example, in order to melt an ice crystal covered by bilayer graphene,
a ~25% larger force is needed to melt the ice compared to monolayer
graphene case (see Figure ​Figure55b). For three layers of graphene, forces larger than 10 nN
are needed to form the quasi-liquid layer. We attribute this behavior
to the increase of the effective tip–graphene contact area
on the ice surface. Thicker graphene cover sheets will convolute the
indentation by the tip more and lead to an increase of the effective
contact area, due to their higher bending modulus66 compared to that of single-layer graphene. Therefore, higher
forces are required in order to reach the pressure needed to melt
the ice crystal (i.e., 6 GPa). The curves perfectly
overlap with each other when compensating for the increase of the
contact area due to the thicker graphene cover (inset of Figure ​Figure55b). This reveals
that the mechanism leading to the observed phase transition is purely
pressure. The extracted contact areas for bilayer and trilayer graphenes
have increased about 2 and 3 times, respectively, compared to single-layer
graphene.

Our information is obtained from friction forces during
scanning,
and the possibility that related heat effects may interfere with the
inherent properties of the considered system needs attention. For
this purpose, we have conducted experiments with different tips (different
radii of curvature and material). The results of the most deviating
measurements are shown in Figure ​Figure55a, obtained with sharp diamond tip (radius of curvature
<5 nm) and those shown in Figure ​Figure66a, obtained with a blunt Si tip (radius of curvature
of 20 nm), both from data gained at room temperature. When accounted
for the different contact areas and the consequently larger forces
required to melt the ice, the same melting characteristics are observed,
and the influence of friction-induced heating on the melting of the
ice crystals is thus clearly excluded. The clearest effect is expected
from the variation of the contact area: a larger contact area leads
to a higher friction force,67 and therefore,
an enhanced heat generation should be expected. Still no differences
are observed for the results obtained with tips with clearly different
radii of curvature, and apparently, the graphene cover sheet warrants
sufficient thermal insulation due to its anisotropic thermal conductivity
discussed above. We can safely conclude that the melting of the ice
is the result of the exerted pressure only.

Phase diagram of confined
water. (a) Areal change as a function
of pressure at different substrate temperatures recorded with the
same PtSi tip, normalized to the maximum quasi-liquid area. At elevated
temperatures, the pressure needed to initiate melting...

Temperature Influence on the Melting Pressure

When
the temperature of the substrate is increased, the applied pressure
required to melt the ice crystals decreases (see Figure ​Figure66a). Because of the higher substrate
temperature, the water molecules gain energy and therefore become
dynamic even at lower pressures.56 As a
result, less pressure is needed to melt the ice crystals. The magnitude
depends strongly on the substrate temperature. For example, at 60
°C, an external pressure of ~2 GPa is needed in order
to melt the ice crystals. Li and Zeng56 predicted that for a monolayer of ice on mica without a graphene
cover, the interfacial hydrogen bonds, that is, the bonds between
the mica and the water molecules, are broken at temperatures around
100 °C. At these temperatures, the ice layer loses its structure
and its net dipole and acts as liquid. These observations explain
the coarser and smoother shaped fractals observed after heating at
100 °C for 1 h in a recent study.53 When the temperature is increased, the fractals undergo edge melting,
and the water molecules at the edges rearrange, resulting in a smoother
and coarser fractal.

It is noted that the critical pressure
for melting, PM, is equal to the summation
of the van der Waals adhesion pressure, PW, and the critical exerted pressure, Pc. The van der Waals adhesion pressure is calculated using PW = EW/d, where EW is the adhesion energy per
unit area and d is the distance between the graphene
cover and the supporting mica.68,69PW is estimated to be approximately 150 MPa for EW ≈ 0.075 J m–236,54 and thus negligibly small. PM as a function
of temperature denotes the coexistence curve between the solid and
the quasi-liquid phases. The functional shape of this curve is given
by the Clausius–Clapeyron relation70

1

where L is the specific latent
heat of fusion, k is Boltzmann’s constant,
and P0 is the equilibrium pressure at
some temperature T0. We have plotted the
ln(PM) per Pa values obtained from data
as shown in Figure ​Figure66a as a function of the corresponding reciprocal temperatures in Figure ​Figure66b. From a first-order
polynomial fit and by using eq 1, we have extracted the specific latent heat of fusion of
water molecules from the quasi-liquid water into the solid ice and
found it equal to 0.15 ± 0.04 eV per water molecule. We emphasize
here that the value is independent of the uncertainty regarding the
critical pressure of melting as the ΔA(P,T) curves have been obtained with the
same tip. This value is only two times larger than the bulk latent
heat of fusion at 0 °C (i.e., 0.062 eV per water
molecule). This correspondence is a strong confirmation of the suggested
mechanism. The phase transition is clearly related to melting of the
confined ice. The difference of the latent heat of fusion in two dimensions
compared to the three-dimensional case is hard to explain and needs
a specialized theoretical consideration, which is lacking at this
moment. This difference is quite subtle in view of the fact that already
in three dimensions the heat of fusion is about 1 order of magnitude
smaller than the heat of vaporization. Interestingly, from our data,
we can extrapolate that at about 100 °C the confined ice layer
undergoes melting at a pressure of ~1 atm, in good agreement
with the result of ref (53). We finally note that the exact value of PM depends on the absolute size of the contact area. Possible
margins have no consequence for the obtain heat of fusion of two-dimensional
ice.

Conclusions

To conclude, the pressure-induced solid
to quasi-liquid phase transition
of confined ice has been explored in situ and real
time using scanning probe microscopies. Two-dimensional ice crystals
trapped between graphene and mica melt and form a quasi-liquid layer
of water when a critical pressure beyond 6 GPa (at room temperature)
is exerted locally onto the system. The H-down ice network loses its
order, and the molecules become dynamic and mobile. The process is
fully reversible; when the applied pressure is lifted, the water molecules
immediately refreeze and resume a polarized H-down network. We were
able to determine the heat of fusion in 2D ice at 0.15 ± 0.04
eV per water molecule. The protective graphene cover transports the
dissipated energy induced by the probing tip effectively away from
the ice crystals such that the melting and refreezing processes are
only governed by pressure. The graphene cover warrants a powerful
thermal protection from the environment. Our results are crucially
important for understanding the phase behavior of confined water,
and they provide an example of intrinsic regelation of 2D ice.

Experimental Section

The graphene
flakes were obtained using the microexfoliation process
from a freshly cleaved HOPG (ZYA grade, MikroMasch) and immediately
deposited on a freshly cleaved mica surface (SPI, V1) at ambient conditions.
The number of graphene layers was determined by optical microscopy
with a DM2500H materials microscope (Leica, Germany) and tapping mode
atomic force microscopy (Agilent 5100 atomic force microscope).53,71 All the experiments were performed inside an environmental chamber
in which the relative humidity (RH) can be controlled. The RH was
measured using a humidity sensor (SENSIRION EK-H4 SHTXX, Humidity
Sensors, Eval Kit, SENSIRION, Switzerland), with an accuracy of 1.8%
between 10 and 90% RH and was controlled by purging the environmental
chamber with an adjustable N2 flow. The sample was heated
using a Peltier element and a Lakeshore 332 temperature controller.
Lateral force microscopy and conductive AFM imaging of the graphene–mica
system was performed at room temperature and in contact mode using
AD-E-0.5-SS tips (diamond tips, Adama Innovations) with a nominal
spring constant of 0.3 N/m and resonance frequency of 30 kHz and PtSiCont
(NanoSensors) with a nominal spring constant of 0.3 N/m and a resonance
frequency of 15 kHz. In order to make electrical contact with the
graphene flakes, for the C-AFM measurements, the graphene flakes were
mechanically connected with a bigger graphite flake acting as an electrode.59

Acknowledgments

The
authors thank the Dutch Organization for Research
(NWO, STW 11431) for financial support.

Supporting Information Available

Movie of the topographic
changes of confined water between
graphene and mica when an external pressure is applied; when the pressure
is increased, the quasi-liquid layer propagates from the edges of
the ice crystal toward the interior; with a decreasing pressure, the
quasi-liquid layer shrinks until it completely disappears when the
pressure drops below the critical melting pressure (AVI)

Movie of a sequence of lateral
force images, recorded
simultaneously with the topography movie, of confined water between
graphene and mica when an external pressure is applied (AVI)

Thomson J.
A Quantitative
Investigation of Certain Relations Between the Gaseous, the Liquid
and the Solid States of Water-Substances. Proc.
R. Soc. London
1873, 22, 27..10.1098/rspl.1873.0005 [Cross Ref]